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# Survival Analysis Project

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### Survival Analysis Project

1. 1. German Breast Cancer Survival Analysis David Schuler, Ankur Verma, Udyot Kumar, Uma Lalitha-Chockalingham
2. 2. Objectives ● Understand the length of time between breast cancer diagnoses and specific events ● Understand what factors play a role in determining these lengths
3. 3. About Survival Analysis ● Predicting the time until an event of interest occurs ● Applications in Medicine, Manufacturing, Sociology, Sports, and many more ● Right Censored Data – an observation where the event has not yet occurred ● Survival Function - probability that at a given time, t, an event of interest has not yet occurred
4. 4. Kaplan-Meier Estimator ● Non-parametric estimator of the survival function ● Time on the X-axis ● Percentage surviving on Y axis ● Tick marks represent right-censored observations
5. 5. Cox Proportional Hazard Regression ● Used to look at the relationship between the survival of a patient and various explanatory variables ● Each explanatory variable is given a coefficient ○ HR = 1 : No effect ○ HR < 1 : Reduction in hazard ( Death) ○ HR > 1 : Increase in Hazard ( Death)
6. 6. German Breast Cancer Data ● Retrieved from UMass Amherst’s Statistics website ● Data collected from clinical trials performed by the German Breast Cancer Study Group ● Total of 686 observations conducted between July 1984 and December 1989 ● 16 variables, including censoring and time-length fields for death and cancer recurrence
7. 7. Exploratory Data Analysis
8. 8. Correlation ● menopause and age ● Estrogen and Progesterone
9. 9. Preliminary Survival Analysis - KM Curves
10. 10. Preliminary Survival Analysis - KM Curves
11. 11. Probability density function f(t) Survival function S(t) = P(T>=t) Hazard function h(t) = f(t) / S(t) A way to compare two hazard functions: Hazard ratio : HR(t) = h0 (t) / h1(t) Proportional hazard assumption : The hazard ratio does not vary with time, i.e. HR(t) = HR
12. 12. Preliminary Survival Analysis - Cox PH ○ HR = 1 : No effect ○ HR < 1 : Reduction in hazard ( Death) ○ HR > 1 : Increase in Hazard ( Death) ● Age1 = [21,30] ● Age2 = (30,50] ● Age3 =(50,80]
13. 13. COX Regression Modelling with phreg in SAS
14. 14. Survival Curve Estimate ( Test Data - 3 rows)
15. 15. Comparing R, Python & SAS Code
16. 16. Comparing R, Python, & SAS: Plots
17. 17. SAS Plot
18. 18. Comparing Regression Models: Tumor Grade
19. 19. Comparing Regression Models: Hormone
20. 20. Comparing Regression Models: Menopause